I'm new to toilet repair. My parents have two old Case 50 toilets, which recently had the hardware in their tanks replaced (I did one, I believe a plumber did the other). Both now have trouble flushing. I'm working on the first, which seems to have four problems:

1. The water level is too low, and I can't seem to figure out how to adjust it.

2. The toilet lever doesn't stay down when you flush, so you have to hold it down for a while (I think this may be caused by the low water level leading to lack of pressure through the valve).

3. The plunger that seals the big tank drain hole in the bottom of the tank sometimes either doesn't fall down at all, or misses the hole, causing the toilet to run.

4. The tank continually runs a very tiny bit down the bowl even when the big drain hole in the tank is sealed. This seems to stop if I pull the ball up by hand (or equivalently, push the plunger valve down)

The hardware has two adjustable screws (one roughly 1/4" in diameter near the inlet, and one roughly 1/2" in diameter after the plunger valve at the end of the ball stick). However, adjusting these screws doesn't seem to have any affect on the toilet operation as far as I can tell. The ball stick is attached with two thumbscrews, which I don't think are meant to be adjusted, but I'm not sure. I've attached some photos of the toilet for reference.

I hope someone out there has some experience with this toilet! I've heard it's a well-made toilet, but I've been fiddling with it for a while and can't seem to make any progress. Also, please excuse me if I'm not using the right language to describe the various parts and issues.

I have 2 Case 3000 toilets that are slow at filling up and I have to lift the ball to stop the toilets from constantly running after being flushed. Is there any advice on how to adjust these? Our well water has a lot of iron and lime deposits. Are there any chemicals I can put in the water tank that will not harm the internal parts and help clean the system?

4. The tank continually runs a very tiny bit down the bowl even when the big drain hole in the tank is sealed. This seems to stop if I pull the ball up by hand (or equivalently, push the plunger valve down)

I have the same leakage problem. But when I pull up on the ball or push down on the valve it stops. Will replacing the plunger assembly solve the problem? Also, how do I get the little white plastic part out that the plunger presses down on? The replacement kit comes with that so I figure I should replace that as well.
Thanks, Steve